Actualism is the doctrine that the only things there are, that have being in any sense, are the things that actually exist. In particular, actualism eschews possibilism, the doctrine that there are merely possible objects. It is widely held that one cannot both be an actualist and at the same time take possible world semantics seriously — that is, take it as the basis for a genuine theory of truth for modal languages, or look to it for insight into the (...) modal structure of reality. For possible world semantics, it is supposed, commits one to possibilism. In this paper I take issue with this view. To the contrary, I argue that one can take possible world semantics seriously without any commitment to possible worlds or possibilism and hence remain in full compliance with actualist scruples. Moreover, one can do so without without invoking either "ersatz" worlds or haecceities. (shrink)

Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The systems S4 and S5 are useful in many different ways. They map out structures that are relevant to a number of different applications. S1, S2 and S3 however, are not so lucky. They are (...) little studied, and used even less. It has become dear that the structures described by S4 and S5 are important in different ways, while the structures described by S1 to S3 are not so important. In this paper, we will see another formal system with a number of different uses. We will examine a substructural logic which is important in a number of different ways. The logic of Peirce monoids, inspired by the logic of relations, is useful in the independent areas of linguistic types and information flow.In what follows I will describe the logic of Peirce monoids in its various guises, sketch out its main properties, and indicate why it is important. As proofs of theorems are readily available elsewhere in the literature, I simply sketch the relevant proofs here, and point the interested reader to where complete proofs can be found. (shrink)